Enhanced approaches to the combination of forecasts

Many important decisions are based on forecasts for the future development of key variables in the field under consideration. Very often the decision-maker has the problem of having more than one forecast for the variables of interest. Instead of selecting one of the forecasts it is a successful strategy and common practice to combine the individual forecasts. The predominant approach is to concentrate on one target variable at a time and to perform a linear combination of the forecasts for that variable. In the book in hand, this standard univariate linear combination approach is enhanced in two respects: Firstly, a linear plus quadratic set-up for the combination of univariate forecasts is introduced as a non-linear combination alternative (univariate linear plus quadratic combination). Similar to a higher order Taylor approximation it may result in more accurate combined prediction. Secondly, several target variables are considered at the same time, and forecasts for such vector valued variables are combined linearly (multivariate linear combination). Thus, additional information is exploited by taking the interactions between the components of target vector and forecasts into account. For each approach the mean square prediction error optimal combination para-meters are derived. To ease implementation of the new methods, appropriate linear regression models are identified. Finally, the enhanced approaches are investigated numerically in terms of their potential, their empirical performance and their results in a simulation study.